# MATLAB Tutorial Session

Updated 2017-10-13

Code and tutorial provided by Madhi Yousefi

## Commands

Every command will have a default return printed onto the screen. Prepending a ; character at the end of the command will disable output, but the command is still executed. (eg. a1 = 4;)

### Useful Commands

clear all		   % clears all variables from workspace
clc				  % clears command window

save('MyVar.mat');      % Save all Workspace variable into MyVar.mat
save('MyVar1.mat','r9') % Save only r9 into MyVar1.mat

delete('MyVar1.mat')    % Delete MyVar1.mat


### Environment

mkdir ../example; 	% makes a directory
cd ../example; 	    % changes directory


### Instance

Variables can be assigned, we don’t need to worry about the type of variable.

C = 'g';	% character
I = 123;	% integer
F = 3.14;	% float


### Basic Math Operators

a1 = 2;
a2 = 5.3;
a3 = 1.2e2;     % 120
a4 = 12e-3;     % 0.012
r1 = a1+a2;     % summation
r2 = a1-a2;     % subtraction
r3 = a1 * a2;   % multiplication
r4 = a1 / a2;   % division
r5 = a2 ^ a1;   % power


### Complex Variables

c1 = 10+12j;
c2 = 12+10i;
r1 = abs(c1);   % absolute value
r2 = imag(c1);  % imagibary part
r3 = real(c1);  % real part


Note that when using i and j, there is no multiplication sign. 5*j is different from 5j.

### Vectors and Matrices

v1 = [2 3 4 5]; 	% 1 by 4 row vector
v2 = [2 3 4 5]'; 	% 4 by 1 column vector
v3 = [2; 3; 4]; 	% 3 by 1 column vector, semicolon (;) seperates columns
v4 = 0:.1:10;   	% a vetor starting form 0 incrementing by .1 upto 10.

% 2 by 3 matrix, semicolon (;) seperates columns, the matirx must be properly defined
m1 = [1 2 3; 3 4 2];

m2 = zeros(3,4);     % 3 by 4 zero matrix
m3 = ones(2,3);      % 2 by 3 matrix with all elements equal to 1;
m4 = eye(2,2);       % 2 by 2 identity matrix
m5 = magic(2);


#### Accessing Elements

v2(3) = dummy1;     % or v2(3,1) = dummy1;
m2(2,1) = dummy2;


#### Matrix Operations

r1 = m1 + m3;       % summation
r2 = m1 - m3;       % subtraction
r3 = m4 * m1;       % multiplication
r4 = m4 ^ 2;        % power, r4 = m4 * m4
r5 = inv(4);        % inverse
m5 = m1';           % Transpose


#### Matrix Element-Wise Operations

If the operations needs to be done with individual corresponding elements, use element-wise operations.

r6 = m1 .* 2;       % multiplying all elements of m1 by 2
r7 = m1 .* m3;      % elementwise multiplication of m1 and m3
r8 = m1 ./ 2;       % deviding all elements of m1 by 2
r9 = m1 .^3;        % elementwise power


## Control

### Loops

#### For Loop

The following example will loop from i=1 to i=10 at a step of 2.

for i = 1:2: 0;
dummy = i^2;
disp(dummy);
end


#### While Loop

m = 0;
while m <= 10;
m = m + 1;
disp(m);
end


### Conditional

m = 1;
if m == 0
disp('m is zero.');
elseif m < 0
disp('m is negative.')
else
disp('m is positive.')
end


## Functions

Here is a function defined by the name of foobar that takes in parameters input1 and input2 and spits outputs output1 and output2.

function [output1, output2] = foobar(input1, input2)
output1 = input1 + input2;
output2 = input1 - input2;
end


## Plotting

In order to plot anything, we first need to specify the signal / data we want to plot. In this case, we are plotting a sin and cos wave.

x = 0:.1:2*pi;
y1 = sin(x);
y2 = cos(x);


### Simple Plot

First we open the plot and pass it the signals desired.

figure(1)               % open a new fiqure
plot(x,y1,'Color','red', 'LineStyle' , ':','LineWidth', 4);


#### Axis Font

set(gca,'FontName','Times');
set(gca,'FontSize',14);


#### Axis Tick-marks

set(gca,'XTick',[0 pi/2 pi 3*pi/2 2*pi]);
set(gca,'XTickLabel',{'0', 'pi/2', 'pi', '3pi/2', '2pi'});


#### Axis Limits

xlim([0 2*pi]);         % or ax.XLim = [0 2*pi]
ylim([-1.5 1.5]);       % or ax.YLim = [-1.5 1.5]


#### Grid

grid on;


If we want to specify the vertical or horizontal grids, then:

ax.XGrid = 'on';
ax.YGrid = 'on';


#### Labels

xlabel('x');            % or ax.XLabel.String = 'x'
ylabel('y_1');          % or ax.YLabel.String = 'y_1'


#### Title

title('sine wave');


### More Variables In the Same Plot

To plot two functions in the same plot, we could use the hold commands and do something like:

figure;
h1 = plot(x,y1,'Color','blue', 'LineStyle' , '--','LineWidth', 4);
hold on
h2 = plot(x,y2,'Color','red', 'LineStyle' , ':','LineWidth', 4);
hold off


Alternatively, we could also use the simplified version (although I think it’s less easy to customize):

plot(x,y1,x,y2)


#### Legends

legend([h1,h2],{'sin','cos'}, 'FontName','Times','FontSize',16)


## Transfer Functions

Suppose we have a transfer function $$G(s)$$ we want to use in MATLAB. The transfer function is given as follows.

$G(s)=\frac{s}{s^2+3s+2}$

To create the transfer function, we use these commands:

num = [1 0];     % numerator of G
den = [1 3 2];   % denumerator of G
G = tf(num,den); % define G, tf(num,den)


Alternatively, you could also do (I like this one)

s = tf('s');
G = s / (s^2 + 3*s + 2)


If we want it in zero-pole-gain representation, we use this command.

G1 = zpk(G);


### Plotting Responses

pzmap(G);       % zero pole plot
impulse(G)      % impulse response
step(G);        % step response
bode(G);        % bode plot
rlocus(G);      % root locus plot
nyquist(G);     % nyquist plot


### Transfer Function Connections

H = tf([1 1],[1 2]);
F = feedback(G,H);  % feedback connection
S = series(G,H);    % or P = G*H, series connection
P = parallel(G,H);  % or P = G+H, parallel connection
Gd = c2d(G,1);      % discretize G, c2d(tf,sampleTime)
Gc = d2c(Gd);       % Convert a discrete model to a continuous model


### Model Simulation

To simulate a model, let us first define the time interval / vector:

t = 0:1:20;	% 0, 1, 2,..., 19, 20


Then we need to define the input:

u = 5*sin(t);


Last we can use lsim to simulate. Then we can plot as usual.

y = lsim(G,u,t);

figure;
subplot(2,1,1)
plot(t,y);      % plot input
ylabel('y');
xlabel('t');
subplot(2,1,2)
plot(t,u);      % plot output
ylabel('u');
xlabel('t');